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Magnetic Resonance Imaging, Computed Tomography, and other technologies of 3D medical imaging are routinely used to visualize a particular structure in the patient s body. The classification of the image region corresponding to this structure is called segmentation. For applications in Neuroscience, it is paramount for the segmentation of a brain scan to represent the brain boundary as a folded surface with no holes. However, in practice, a brain scan segmentation generally exhibits many erroneous holes. To address this issue which affects Medicine, Graphics and Industrial Design, I focused my PhD work on developing an algorithm for automatically correcting holes in 3D scanned data. Upon concepts of Discrete Topology and Computational Geometry, my topology simplification algorithm built upon the construction of front propagations and Reeb graphs. Based on experiments with clinical data, I proved that my algorithm successfully corrected the erroneous holes with high accuracy and low complexity even for images that exceeded the computer main memory. To enable radiologists to obtain a correct segmentation, I made the software that I developed available at http://www.opentopology.org.